All the solutions provided in McGraw Hill Math Grade 5 Answer Key PDF Chapter 1 Lesson 5 Understand Place Value will give you a clear idea of the concepts.
McGraw-Hill My Math Grade 5 Answer Key Chapter 1 Lesson 5 Understand Place Value
Draw It
Use models to describe the relationship between the value of the digits in the decimal 0.77 and their place-value position.
Question 1.
Use models.
Shade the model to show 0.77. Write the decimal in word form and standard form.
Word form: seventy- ___ hundredths
Standard form: 0.77
The place-value chart that you used for whole numbers can be extended to include decimals.
Write the decimal 0.77 in the place-value chart.
Answer:
We shaded the 77 hundredths in the above-given cube.
In word form, we can write as seventy-seven hundredths.
In fractions, we can write as 77/100
Now we have placed them in the correct position.
Question 2.
Describe the relationship.
The value of the digit 7 in the tenths place is 0.7 or ___ tenths.
The value of the digit 7 in the hundredths place is 0.07 or ____ hundredths.
Use a calculator to find 0.7 ÷ 0.07. ____
The value of the digit 7 in the tenths place is ____ times as much as the value of the digit 7 in the hundredths place.
The value of the digit 7 in the hundredth place is 
times as much as the value of the digit 7 in the tenths place.
Answer:
– The value of the digit in the tenth place is 0.7 or seven-tenths.
– The value of the digit 7 in the hundredth place is 0.07 or seven hundredths.
– In the third blank, we need to use the calculator to divide the given problem.
7/10 / 7/100
If we calculate this,
7/10 x 100/7 { 7 and 7 gets cancel}
And finally, the answer is 10.
– The value of the digit 7 in the tenth place is 10 times as much as the value of the digit 7 in the hundredth place.
– The value of the digit 7 in the hundredth place is 1/10 times as much as the value of the digit 7 in the tenths place.
Try It
Describe the relationship between the value of the digits in the decimal 0.027 and their place-value position.
Question 1.
Use a place-value chart.
Write the decimal in the place-value chart.
Answer:
The above-given model is the cube of a thousandth.
Already given in question 0.027
The place values of decimals are slightly different from the place value of whole numbers. The value of the digits decreases from the decimal point to the right of the decimal number. The numbers to the right of the decimal number are called the fractional part. The digit immediately after the decimal point is the tenth place, followed by the hundredths place, the thousandths place, the ten thousandths and hundred-thousandths place.
Question 2.
Describe the relationship.
The digit in the thousandths place is ____.
It has a value of ____.
If this digit were to move to the hundredths place, it would have a value of ___.
If this digit were to move to the tenths place, it would have a value of
The digit in each place has a value that is \(\frac{1}{10}\) times as much as it has in the place to its left.
Answer:
The above-given decimal value is 0.027
The digit in the thousandth place is 7
It has a value of 0.007
If the digit 7 is moved to the hundredth place then the value is 0.07
If the digit 7 is moved again to the tenth place then the value is 0.7
Talk About It
The decimal model shows 0.033. Use this decimal to answer Exercises 1—4.
Question 1.
What is the value of the 3 in the hundredth place?
Answer:
The above-given decimal is 0.033
Here asked, the value of 3 in the hundredth place.
So, the value is 0.03
Question 2.
What is the value of the 3 in the thousandth place?
Answer:
The value of 3 in the thousandth place is 0.003
Question 3.
The digit in the hundredth place is how many times as much as the digit in the thousandth place?
Answer:
The digit in the hundredth place is 10 times bigger than the digit in the thousandth place.
300 x 10 = 3000
Question 4.
Mathematical PRACTICE 2 Use Number Sense How many times as great is the value of the digit in the thousandth place as in the hundredth place?
Answer: 1/10 times
Explanation:
from left to right we always multiply with 1/10
from right to left we always multiply with 10
Practice It
Use each model to write a decimal ¡n standard form and word form. Then complete each sentence.
Question 5.
The value of the digit in the tenths place is ___ times as much as the digit in the hundredth place.
Answer:
We need to write the standard form and the word form.
Count the number of boxes is shaded
The above-given model is the hundredth cube.
There are 55 boxes shaded.
So, the fraction will be 55/100
The standard form is 0.55
The word form is a fifty-five hundredth.
The value of the digit in the tenths place is 10 times as much as the digit in the hundredth place.
Question 6.
The value of the digit in the hundredth place is _______ times as much as the digit in the tenths place.
Answer:
The above-given model is the hundredth cube.
Count the number of boxes shaded.
There are 99 boxes that are shaded.
So, the fraction can be written as 99/100
The standard form is 0.99
The word form is ninety-nine hundredth.
The value of the digit in the hundredth place is 1/10 times as much as the digit in the tenth place.
Question 7.
The value of the digit in the thousandth place is ___ times as much as the digit in the hundredths place.
Answer:
The above-given model is the cube of the thousandth
Count the number of boxes shaded.
There are 22 boxes that are shaded.
The fraction can be written as 22/1000
The standard form is 0.022
In word form, we can write as twenty-two thousandth.
The value of the digit in the thousandth place is 1/10 times as much as the digit in the hundredth place.
Question 8.
The value of the digit in the hundredths place is ___ times as much as the digit in the thousandths place.
Answer:
The above-given model is the cube of the thousandth
Count the number of boxes shaded.
There are 44 boxes that are shaded.
The fraction can be written as 44/1000
The standard form is 0.044
In word form, we can write as forty-four thousandth.
The value of the digit in the hundredth place is 10 times as much as the digit in the thousandth place.
Apply It
Question 9.
Micah asked for directions to a local park. He was told to go 0.33 miles south to get to the park. The value of the digit in the tenths place is how many times as much as the value of the digit in the hundredth place?
Answer:
The above-given miles: 0.33
The value present in the tenth place is 3
from the tenth place, we need to check the value of the digit in the hundredth place.
The value of the digit in the tenth place is 10 times as much as the value of the digit in the hundredth place.
Question 10.
Mathematical PRACTICE 2 Use Number Sense In science class, Abigail’s frog weighed 0.88 kilograms. What is the value of the digit in the tenth place?
Answer:
The above-given decimal value is 0.88 kg
Here asked, the value present in the tenth place.
The value of the digit in the tenths place is 0.8
Question 11.
Mathematical PRACTICE 8 Look for a Pattern For the decimal 0.555, the value of the digit in the tenth place is how many times as much as the value of the digit in the thousandth place?
Answer: 100 times bigger
Explanation:
10 x 10 = 100
Therefore, the value of the digit in the tenth place is 100 times as much as the value of the digit in the thousandth place.
Question 12.
Look at the place-value chart. What happens to the value of the digit 2 as it moves places to the left from the thousandth place?
Answer:
The value of the digit in the tenth place is 0.2
The value of the digit in the hundredth place is 0.02
The value of the digit in the thousandth place is 0.002
Every time the value is 10 times bigger.
Write About It
Question 13.
How are the place-value positions to either side of a particular number related?
Answer:
The place value positions to either side of a number are related because they are 10 times smaller or ten times bigger – a number in the hundreds column is ten times bigger than the same number in the tens column, for example. Each place has a value of 10 times the place to its right.
McGraw Hill My Math Grade 5 Chapter 1 Lesson 5 My Homework Answer Key
Question 1.
The model shows a decimal. Write the decimal.
Word form: eighty-eight hundredths
Standard form: 0.88
Answer:
The above-given model is the hundredth cube.
There are 88 boxes shaded.
The fraction can be written as 88/100
Question 2.
Write the decimal in the place-value chart.
Answer:
The place value of the digit in the tenths place is 0.8
The place value of the digit in the hundredth place is 0.08
Using the decimal place value chart, we can write the place values of all the numbers. 6 comes under the hundreds column, therefore, the place value of 8 is 8 hundred, or 8 × 100 = 800; 8 comes under the tens column, therefore, the place value of 8 is 8 tens, or 8 × 10 = 80
Question 3.
The value of the digit 8 in the tenth place is 0.8.
The value of the digit 8 in the hundredth place is 0.08.
The value of the digit 8 in the tenth place is 10 times as much as the value of the digit 8 in the hundredth place.
The value of the digit 8 in the hundredth place is \(\frac{1}{10}\) times as much as the value of the digit 8 in the tenth place.
Answer:
Practice
Question 1.
Use the model to write a decimal in standard form and word form. Then complete the sentence.
The value of the digit in the hundredth place is ___ times as much as the digit in the tenth place.
Answer:
The above-given model is the hundredth cube.
Count the number of boxes that are shaded.
There are 11 boxes are shaded.
The fraction is 11/100
In decimal, we can write it as 0.11
The word form is eleven-hundredth
The value of the digit in the hundredth place is 10 times as much as the digit in the tenth place.
Question 2.
Use the model to write a decimal in standard form and word form. Then complete the sentence.
The value of the digit in the thousandth place is ___ times as much as the digit in the hundredth place.
Answer:
The above-given model is the cube of a thousandth.
Count the number of boxes that are shaded.
There are 66 boxes that are shaded
The fraction is 66/1000
In decimal, we can write it as 0.066
The word form is sixty-six thousandth
The value of the digit in the thousandth place is 10 times as much as the digit in the hundredth place.
Problem Solving
Question 3.
Michael bought 0.44 pounds of sliced turkey. What is the value of the digit in the hundredth place?
_____________________
The value of the digit in the hundredth place is how many times as much as the value of the digit in the tenth place?
_____________________
Answer:
The above-given decimal: 0.44
The value of the digit in the hundredth place is 0.04
The value of the digit in the hundredth place is 10 times as much as the value of the digit in the tenth place.
Question 4.
A small piece of metal weighs 0.77 grams. What is the value of the digit in the tenth place?
_____________________
The digit in the tenth place is how many times as much as the value of the digit in the hundredth place?
_____________________
Answer:
The above-given decimal: 0.77
The value of the digit in the tenths place is 0.7
The digit in the tenths place is 1/10 times as the value of the digit in the hundredth place.
Question 5.
Mathematical PRACTICE 2 Use Number Sense Write a decimal where the value of a digit is \(\frac{1}{10}\) as much as a digit in another place.
Answer:
The above-given fraction is 1/10
In decimal form, we can write it as 0.1
The other place would be the hundredth place.
The value of the digit in the hundredth place is 0.01